Effectiveness of Sparse Data Structure for Double-Double and Quad-Double Arithmetics

Double-double and Quad-double arithmetics are effective tools to reduce the round-off errors in floating-point arithmetic. However, the dense data structure for high-precision numbers in MuPAT/Scilab requires large amounts of memory and a great deal of the computation time. We implemented sparse data types ddsp and qdsp for double-double and quad-double numbers. We showed that sparse data structure for high-precision arithmetic is practically useful for solving a system of ill-conditioned linear equation to improve the convergence and obtain the accurate result in smaller computation time.